Abstract
Coupled free-flow and porous-medium systems appear in a variety of industrial and environmental applications. Fluid flow in the free-flow domain is typically described by the (Navier–)Stokes equations while Darcy’s law is applied in the porous medium. The correct choice of coupling conditions on the fluid–porous interface is crucial for accurate numerical simulations of coupled problems. We found out that the Beavers–Joseph interface condition, which is widely used not only for fluid flow parallel to the porous layer but also for filtration problems, is unsuitable for arbitrary flow directions. To validate our statement, we provide several examples and compare numerical simulation results for the coupled Stokes–Darcy problems to the pore-scale resolved models. We show also that the Beavers–Joseph parameter cannot be fitted for arbitrary flow directions.
Highlights
Coupled flow systems containing a porous-medium layer surrounded by a free-fluid region appear in various environmental settings, biological and technical applications such as interaction of surface water with groundwater, filtration processes and transport of therapeutic agents in blood vessels and tissues
The correct choice of interface conditions is crucial for accurate numerical simulations of coupled porous-medium and free-flow problems
The geometrical configuration of the porous medium is often assumed to be very simple, e.g. made up of circular inclusions which are structured in rows and columns in line, and the fluid flow parallel to the fluid–porous interface
Summary
Coupled flow systems containing a porous-medium layer surrounded by a free-fluid region appear in various environmental settings, biological and technical applications such as interaction of surface water with groundwater, filtration processes and transport of therapeutic agents in blood vessels and tissues. We consider the classical coupled problem consisting of the Stokes equations in the free-flow domain, the single-phase Darcy’s law in the porous medium and the conservation of mass, the balance of normal forces and the Beavers–Joseph coupling condition (Beavers & Joseph 1967) at the fluid–porous interface. The goal of this work is to demonstrate that the widely used Beavers–Joseph and Beavers–Joseph–Saffman interface conditions fail for arbitrary flow directions and to provide a benchmark which can be used by researchers working on the development of alternative interface conditions for coupled free-flow and porous-medium systems (Carraro et al 2015; Lacis & Bagheri 2017; Lacis et al 2019).
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